There are many well-known methods for the optical testing of samples. Interferometry is one of these methods.
For interferometric surface testing, beams of light from a source such as a laser are reflected by an object surface and by a reference surface and then superimposed in a manner such that they interfere with each other. This creates a brightness pattern containing information regarding deviations of the object surface from the reference surface. This brightness pattern is recorded by a camera.
Interferometric testing can also use transmitted light. That is, the light beam is divided into a measuring beam and a reference beam, and the measuring beam is passed through the transparent sample. The two paths of rays are then superimposed such that they interfere with each other, and the resulting brightness pattern is recorded by a camera.
Camera images of the brightness pattern are evaluated by, first, computing phase values for each image point recorded by the camera and, then, using those computed phase values to create a phase diagram or chart of the imaged sample. Several different methods are known for computing these phase values. A good overview of a number of these methods, as well as their advantages and disadvantages, appears in a well-known thesis by B. Dorband (1986), University of Stuttgart.
When information is in the form of periodic brightness patterns, the phase value of the relative brightness recorded for a particular image point can only be computed in modulo 2.pi., i.e., to an unknown integral multiple of the number 2.pi.. If this unknown integral multiple is set equal to zero, and even if it is assumed that the sample surface is not irregular, so-called "discontinuities" (sudden changes) occur in the phase images. At such discontinuities, the difference between the computed phase values of adjoining points has an absolute value greater than the number .pi.. In order to determine the contours of the sample surface (or the deviations of the sample from a reference element), the integral multiple of 2.pi. must be determined, i.e., the so-called discontinuity must be eliminated.
One known method of discontinuity elimination has Abeen described by K. Itoh, Applied Optics, Vol. 21, No. 14, page 2470 (1982). In the first step of this method, the differences between the phase values of adjacent points of a camera image are computed. Based on the sampling theorem, these quantitative differences must be less than .pi. in order to identify those discontinuities in which the difference is quantitatively greater than .pi.. Therefore, where such discontinuities occur, the number 2.pi. is added to or subtracted from the differences in such a manner that the corrected differences between the phase values range between -.pi. and +.pi. and, thus, are expressed in terms of modulo 2.pi.. By integrating these modulo 2.pi. phase differences over the phase image, ultimately a phase chart with corrected discontinuities is attained. For such a phase chart, the integral multiple of the number 2.pi. has been determined and, therefore, deviations of the object surface from the reference surface (or of the sample from a reference element) can be computed clearly.
Numerous other publications, among them German Patent No. DE-OS 36 00 672 and European Patent No. EP 0 262 089, have disclosed measuring systems in which a bar pattern is projected onto the object surface and the projected bar pattern is recorded by a camera. The contours of the object surface lead to a deformation of the bar pattern recorded by the camera. The evaluation of the camera image is analogous to the evaluation of an interferometrically generated brightness pattern. Namely, the brightness of each point of the camera image is first used to compute a phase value of the bar pattern, and then the calculated phase values are composed to form a phase image. However, this phase image also has discontinuities because, in turn, these phase values can be computed only up to an integral multiple of the number 2.pi..
In such testing systems, statistical measuring errors which are caused, for example, by detector noise or air turbulences in the optical paths can be reduced by averaging many individual measurements. However, the computed phase values cannot be averaged before the discontinuities are eliminated. The reason for this is that the sampling theorem, after averaging, can no longer be used to identify discontinuities. Therefore, K. Itoh notes in his above-cited paper that averaging can only be done by using phase charts from which discontinuities have already been eliminated.
Unfortunately, the computation of phase charts from which discontinuities have been removed, i.e., eliminated, is a relatively time-consuming process, since each point of the phase image requires at least one integration. This computational effort is substantially greater if the initially computed phase values are tested among each other at different points of the phase image and, in addition, are checked as to their consistency relative to each other, as has been described in Journal of the Optical Society of America, Vol. 4, No. 1, page 267 (1987). When averaging, this use of time increases in proportion to the number of phase images used for averaging. Therefore, in order to achieve a distinct reduction in statistical errors, very long measuring and computation times are required because statistical errors, as is well known, decrease inversely proportional to the square root of the number of averaged phase images.
The present invention provides a measuring system which, while similar to those just described above, permits the averaging of a plurality of phase images (to achieve a desired reduction in statistical errors) in a remarkably shorter time.